Progressive Geometry Compression

1. Progressive Geometry Compression Zhu Ping 2006.12.06

2. Compression Necessity: 1. Storage; 2. Transmission Base: Information Theory

3. Coding Techniques • Huffman coding • Arithmetic coding • VQ coding • LZW coding

4. Geometry Compression • Geometry Compression. Siggraph 95 Michael Deering Sun Microsystems an engineer in Java 3D API Interest:virtual reality

5. Triangle Strip

6. Generalized Triangle Strip • Vertice buffer • Old vertice • New vertice

7. Generalized Triangle Mesh

9. Cost: 1. Mesh Buffer 2. Push Selected(one more bit) 3. Reuse Vertice from Buffer

10. Progressive Mesh • Progressive Mesh. Siggraph 96 Huges Hoppe. Progressive Procession: Mn Mn-1+Wn Mn-1 predition P Wn Mn=Mn-1+(P(Mn-1)+wn)) {M0,wn,…w1}

11. Progressive Compression of Arbitary Trianglar Meshes • Progressive Compression of Arbitary Trianglar Meshes IEEE Visualization 99. Daniel Cohen-Or David Levin Offir Remez Levin:a professor inSchool of Mathematical Sciences Tel Aviv University,Israel Interest:Subdivision,Image Processing,CAGD, Computer Graphics

12. The 4-color encoding scheme

13. The 2-color encoding scheme

15. Codec Design • Input SN eN’ eN 量化器 编码器 ＋ － ＋ ＋ 发送端 信道 预测器 SN‘ eN’ 输出 解码器 SN‘ 接收端 预测器 S’‘N

16. Mesh Optimization • Mesh Optimization . Siggraph 93 Hugues Hoppe Tony DeRose Tom Duchamp Hoppe:a professor in University ofWashington,now in Graphics Group of Microsoft. 2 ACM TOGs in 06y 2 ACM TOGs in 05y 4 ACM TOGs in 04y Graphics Award in Siggrpah

17. Interest:Mesh Simplicial,Compression, Texture synthesis • Question: 网格优化：指作表面网格的优化，通过删除 和插入一些点，使得表面网格在曲率较大的 地方网格较密，光滑平坦处网格单元较大。 目的是合理布置网格的密度，提高单元格的质量。

18. Mesh Representation

19. Mesh Simplicial

20. Mesh Energy Function

22. Application： Surface Reconstruction； Mesh Simplification

23. Geometric Compression For Interactive Transmission • Geometric Compression For Interactive Transmission. IEEE Visualization 2000 Olivier Devillers Pierre-Marie Gandoin INRIA Sophia Antipolis ,France Overview: the topology of mesh can often be reconstructed from its vertices geometry-centric

24. Analysis

26. The cost of bits

27. Coding and Prediction • 1. Arithmetric Coding • 2. Prediction

28. Topology Coding

30. Experimental Results

31. Progressive Lossless Compression of Arbitrary Simplical Complexes • Progressive Lossless Compression of Arbitrary Simplical Complexes. ACM TOG 2002 Pierre-Marie Gondoin Olivier Devillers Related: [Devillers and Gandoin 2000] [Popovic and Hoppe 1997]

32. Geometry Driven Approach:kd-tree

33. Progressive Simplicial Complexes Jovan Popovic Hugues Hoppe Siggraph 97

35. Analysis:

37. Prediction

38. Results:

39. Future Work: Polygonal Meshes

40. Future Work: Polygonal Meshes

41. Thank You !!